Today Sir David warned costs for the £50bn scheme could spiral if it was mired in planning and consultation regulations as "time is money."

In the report Sir David also recommends a larger development of Euston Station than previously planned and scrapping the proposed link between HS2 and the HS1 line, which links St Pancras Station to the Channel Tunnel.

In his report, HS2 Plus, the former London Olympics chief says the infrastructure project is “vital for the future of the country”, improving connections between major cities in the north as well as links to London and closing the economic divide between north and south.

He adds that the government should “accelerate phase two as soon as possible”, extending the track 43 miles north of Birmingham to Crewe by 2027, six years earlier than under current plans.

“It is the right strategic answer, and not just for the area around Crewe: it would also deliver the benefits of HS2 – in terms of better services to the North – much sooner,” he says, and that adding the necessary legislation would not be a “lengthy process”.

Starting construction in the north earlier is a “bigger priority and will deliver more benefits to more people across the country” than the proposed link between HS2 and the HS1 line, he adds.

The government should “consider whether the cost – at around £700 million – is good value or whether it would be better to consider an alternative,” he says.

The report recommends a larger development of Euston Station than currently planned, with the potential for extra income from private retail and commercial developments similar to those at St Pancras and King’s Cross.

Patrick McLoughlin, the Transport Secretary, recently admitted the mammoth hybrid bill giving legislative approval for the London to Birmingham phase of the project is unlikely to clear Parliament before the next election.

In his report Sir David says: “There is a direct connection between the length of time the Parliamentary process takes, and the amount of contingency that is required.

“Additional time spent debating the legislation will translate into extra uncertainty about the construction timescale – and therefore about its cost.”

Sir David told BBC Radio Four’s Today programme: “time is uncertainty; uncertainty leads into cost and eventually money.

He added: “Compared to previous planning process –terminal five took five years to get through the planning process, Crossrail One took three years in just committee stages, so the history is not good. My message to Government, and the public, is infrastructure is critical to this nation and we can’t have a log jam in approval process.

“I understand the reason for debate and proper consultation but time is money.”

Ed Balls, the shadow chancellor, said Labour would back the project if costs could be shown to have decreased, but in his report Sir David said it would be “irresponsible” to reduce the £7 billion contingency set aside for the first phase of the project.

It remains possible that the budget could be lowered in future but “only when the legislative timetable becomes clearer and more certain,” he said.

A Department for Transport spokesperson said the report “confirms that HS2 is the right project at the right price”. The Transport Secretary will issue a full response to Parliament today.

Richard Houghton of HS2 opposition group HS2 Action Alliance said: "Bringing forward work will not be as simple as it sounds. Unless there are plans to circumnavigate the statute book, then a separate Hybrid Bill will have to be introduced and passed for any work other than that detailed in the Phase 1 Hybrid Bill.

“Phase 1 consultation has run to thousands of pages, consultation processes have been questionable and rushed, [and] the Transport Secretary has said it is unlikely to be passed in this Parliament.”